Session and Application variable :) Application variable
as avaiable as it is, as this is application based. where is sessions are not
availabe OOB, they need some extra effort. Reason being if number of sessions
are increased due ot scalibility you will never know from where it is being
excuted. so the answer is to use SQL based session.

DB Connection is very basic and easilyt avaiable. for session you need to find
some alternate or user SQl based session. Below I am posting very basicHelloword with ADFS authentication.

Below are the minimum items needed -

One certificate which is uploaded on Windows Azure as well. .pfx file

Location for ADFS2.0 server as this will provide your claims.

Adding relying party on ADFS2.0 server, which means telling ADFS server "the
request will come form this site, and provide claims for it"

Within Application following changes are needed -

Changes in Application_OnStart [Adding two events associated to Authentication]